Macos – Error while trying to update brew package manager

It sounds like half of it updated before it errored out, and now it's in a bad state. You may want to

cd /usr/local && git reset --hard HEAD

That should reset all git-controlled files (e.g. homebrew) back to their pristine versions. You may need to sudo that git command. After that, you can attempt to fix the permissions however you want (this may be as simple as running sudo chown -R yourname:staff /usr/local if no files in that dir need to be owned by someone else).

Don't forget to fetch the origin:

cd /usr/local/Homebrew
git fetch origin
git reset --hard origin/master

What happens is that you are trying to update brew, but brew itself is either not up to date (likely), there is a permissions change via some OS update (also likely), or brew is slightly corrupt (unlikely). Since brew itself is a git repo, you have to update or reset brew to the master branch version. brew [by default] is located in the /usr/local/Homebrew folder, so you

1. Go to that folder [first command] which also should update permissions (if not see below)
2. Fetch the origin [second command] which means to update your LOCAL version of the remote branch of brew
3. Hard reset [3rd command] based on the REMOTE master branch (which also uses your current permissions).

You can also chown the first command if you are in a non sudo or admin profile

sudo chown -R `whoami` /usr/local/Homebrew
cd /usr/local/Homebrew
git reset --hard origin/master

To understand git reset, take a look at this article.